All toric Kahler surfaces with twistor 2-forms
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909758869471232 |
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| author | Ovchinnikov, Sergei G. |
| author_facet | Ovchinnikov, Sergei G. |
| contents | We complete the classification of all smooth 4-dimensional Kahler geometries admitting a twistor (conformal Killing-Yano) 2-form invariant under a 2-torus action. We establish that there are six geometrically distinct families, and we provide them in a simple form amenable to calculations and compute their curvature. We also find that for toric geometries the square norm of the twistor 2-form is quadratic in moment maps, and we are led to conjecture that this holds when less symmetry is present. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_21114 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | All toric Kahler surfaces with twistor 2-forms Ovchinnikov, Sergei G. High Energy Physics - Theory General Relativity and Quantum Cosmology Differential Geometry 53B35 (Primary), 32Q15 (Secondary) We complete the classification of all smooth 4-dimensional Kahler geometries admitting a twistor (conformal Killing-Yano) 2-form invariant under a 2-torus action. We establish that there are six geometrically distinct families, and we provide them in a simple form amenable to calculations and compute their curvature. We also find that for toric geometries the square norm of the twistor 2-form is quadratic in moment maps, and we are led to conjecture that this holds when less symmetry is present. |
| title | All toric Kahler surfaces with twistor 2-forms |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Differential Geometry 53B35 (Primary), 32Q15 (Secondary) |
| url | https://arxiv.org/abs/2412.21114 |